If $[x]^2-5[x]+6=0$,where $[\cdot]$ denotes the greatest integer function,then $x$ belongs to:

Let $\rho$ be a relation defined on the set of natural numbers $N$, as $\rho = \{(x, y) \in N \times N: 2x + y = 41\}$. Then the domain $A$ and range $B$ are:

The domain of the function $f(x) = \frac{1}{\log_{10}(1-x)} + \sqrt{x+2}$ is

The domain of the definition of the function $f(x) = \frac{1}{4 - x^2} + \log(x^3 - x)$ is

If the domain of the function $f(x) = \cos^{-1}\left(\frac{2-|x|}{4}\right) + (\log_e(3-x))^{-1}$ is $[-\alpha, \beta) \setminus \{\gamma\}$,then $\alpha + \beta + \gamma$ is equal to:

If $x \in \mathbb{R}$,then the range of $\frac{x}{x^2-5x+9}$ is